benchmark_results.json

{
  "summary": {
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    "factual_count": 22,
    "hallucination_count": 24,
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      "threshold_0.6": 0.6087
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    "best_threshold": "0.6",
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  "categories": {
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  },
  "raw_data": [
    {
      "category": "factual_science",
      "text": "Water molecules consist of two hydrogen atoms and one oxygen atom, forming H2O.",
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    {
      "category": "factual_science",
      "text": "The speed of light in a vacuum is approximately 299,792,458 meters per second.",
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    {
      "category": "factual_science",
      "text": "DNA carries genetic information through sequences of four nucleotide bases: adenine, thymine, guanine, and cytosine.",
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    {
      "category": "factual_science",
      "text": "Gravity causes objects with mass to attract each other, as described by Newton's law of universal gravitation.",
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      "text": "Photosynthesis converts carbon dioxide and water into glucose and oxygen using sunlight.",
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      "category": "factual_science",
      "text": "Electrons orbit the nucleus in discrete energy levels, not continuous paths.",
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    {
      "category": "factual_science",
      "text": "The second law of thermodynamics states that entropy in an isolated system tends to increase.",
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    {
      "category": "factual_math",
      "text": "The Pythagorean theorem states that in a right triangle, a\u00b2 + b\u00b2 = c\u00b2, where c is the hypotenuse.",
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    {
      "category": "factual_math",
      "text": "Pi (\u03c0) is the ratio of a circle's circumference to its diameter, approximately 3.14159.",
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    {
      "category": "factual_math",
      "text": "The golden ratio \u03c6 equals (1 + \u221a5) / 2, approximately 1.618033988749895.",
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    {
      "category": "factual_math",
      "text": "Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves.",
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    {
      "category": "factual_math",
      "text": "The sum of angles in a triangle equals 180 degrees in Euclidean geometry.",
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    },
    {
      "category": "factual_math",
      "text": "Euler's identity states that e^(i\u03c0) + 1 = 0, connecting five fundamental constants.",
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    },
    {
      "category": "hallucinations_science",
      "text": "Water is actually composed of three hydrogen atoms and two oxygen atoms, forming H3O2.",
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    {
      "category": "hallucinations_science",
      "text": "The speed of light varies significantly based on the observer's mood and emotional state.",
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    {
      "category": "hallucinations_science",
      "text": "DNA stores information using seven different nucleotide bases including mysterion and phantasine.",
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    {
      "category": "hallucinations_science",
      "text": "Gravity only affects objects painted blue, while red objects float naturally.",
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    {
      "category": "hallucinations_science",
      "text": "Photosynthesis primarily occurs at night when plants absorb moonlight energy.",
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    },
    {
      "category": "hallucinations_science",
      "text": "Electrons are tiny conscious beings that choose their orbital paths based on preference.",
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    {
      "category": "hallucinations_science",
      "text": "Entropy can spontaneously decrease in isolated systems if you believe hard enough.",
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    {
      "category": "hallucinations_math",
      "text": "The Pythagorean theorem proves that a\u00b2 + b\u00b2 = c\u00b3 in all triangles regardless of angles.",
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    },
    {
      "category": "hallucinations_math",
      "text": "Pi equals exactly 3.2 as proven by the Indiana Pi Bill of 1897.",
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    },
    {
      "category": "hallucinations_math",
      "text": "The golden ratio \u03c6 equals exactly 1.5 and was invented by Leonardo DiCaprio.",
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    {
      "category": "hallucinations_math",
      "text": "All prime numbers are even, except for the number 2 which is odd.",
      "score": 0.519,
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    },
    {
      "category": "hallucinations_math",
      "text": "The sum of angles in a triangle equals 360 degrees in all geometries.",
      "score": 0.5584,
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    {
      "category": "hallucinations_math",
      "text": "Euler's identity was disproven in 2019 by quantum computers.",
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    {
      "category": "hallucinations_confident",
      "text": "According to a 2024 Stanford study, humans only use 10% of their brain capacity.",
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    },
    {
      "category": "hallucinations_confident",
      "text": "The Great Wall of China is the only man-made structure visible from the Moon with the naked eye.",
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    {
      "category": "hallucinations_confident",
      "text": "Einstein failed math in school, proving that grades don't matter for genius.",
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    {
      "category": "hallucinations_confident",
      "text": "Goldfish have a 3-second memory span, which is why they seem surprised by their bowl.",
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    {
      "category": "hallucinations_confident",
      "text": "We swallow an average of 8 spiders per year while sleeping.",
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    {
      "category": "hallucinations_confident",
      "text": "Lightning never strikes the same place twice due to electromagnetic memory.",
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    },
    {
      "category": "coherent_reasoning",
      "text": "Because water expands when it freezes, ice floats on liquid water. This property is crucial for aquatic life survival in winter.",
      "score": 0.6813,
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      "category": "coherent_reasoning",
      "text": "If all mammals are warm-blooded, and dolphins are mammals, then dolphins must be warm-blooded.",
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      "category": "coherent_reasoning",
      "text": "The emergence of consciousness from neural activity suggests that complex information processing can give rise to subjective experience.",
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    {
      "category": "coherent_reasoning",
      "text": "Since entropy tends to increase in closed systems, perpetual motion machines that produce energy are thermodynamically impossible.",
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      "category": "coherent_reasoning",
      "text": "Pattern recognition in nature follows mathematical principles because mathematics describes the structural relationships inherent in physical reality.",
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    {
      "category": "incoherent_rambling",
      "text": "The purple elephant mathematics dancing through quantum yesterday because therefore sandwich implications.",
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    },
    {
      "category": "incoherent_rambling",
      "text": "If we consider the aforementioned paradigm shift in the contextual framework of synergistic blockchain AI methodologies going forward.",
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      "resonance_delta": 0.0131,
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    },
    {
      "category": "incoherent_rambling",
      "text": "Studies show that 78.3% of statistics are made up on the spot by experts who claim authority.",
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      "resonance_delta": 0.0682,
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    },
    {
      "category": "incoherent_rambling",
      "text": "The vibrational frequency of crystal healing aligns your chakras with the quantum field of universal consciousness energy.",
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      "resonance_delta": 0.03,
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    },
    {
      "category": "incoherent_rambling",
      "text": "By leveraging our core competencies in disruptive innovation, we can synergize cross-functional deliverables.",
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      "resonance_delta": 0.0774,
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      "category": "phi_resonant_truths",
      "text": "The fine structure constant \u03b1 \u2248 1/137 governs electromagnetic interactions in the universe.",
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      "text": "Consciousness emerges from the coherent integration of information across neural networks.",
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      "text": "The golden ratio appears in nature because it represents optimal packing and growth patterns.",
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      "text": "Information is physical - it requires energy to process and entropy to erase.",
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}